Britain will not accept an EU withdrawal deal without a “precise” political declaration setting out how its requirements on trade and security will be delivered, Theresa May has told her Cabinet.

The Prime Minister was speaking a week ahead of a crunch Brussels summit on October 17-18, at which it had initially been hoped the withdrawal deal would be finalised.

But a deal next week remains far from certain, despite optimistic comments from senior EU figures over recent days, with Mrs May making clear that agreement has not yet been reached on the key issue of the Irish border.

DUP leader Arlene Foster – whose MPs prop up the minority Conservative administration in the Commons – closed down one mooted avenue for compromise by insisting her party will not accept customs or regulatory checks on goods travelling in either direction between Northern Ireland and Great Britain.

Reports had suggested that deadlock over the so-called “backstop” arrangements for Ireland could be broken by permitting checks on exports from the mainland to the north, but not in the opposite direction.

“There cannot be any customs or regulatory barriers between ourselves and the rest of the United Kingdom, both ways,” said Mrs Foster following talks with EU chief negotiator Michel Barnier in Brussels.

“It’s not just a case of regulations between Northern Ireland and GB, it’s also between GB and Northern Ireland. We’ve made that very clear. The Prime Minister understands our position and I expect her to respect that position.”

Mrs May told the regular weekly Cabinet meeting at 10 Downing Street that talks to finalise a withdrawal deal were continuing “on an intensive basis”.

Her official spokesman said: “The PM said that our efforts will focus on seeking agreement on the few remaining issues, including the Northern Ireland backstop.

“She made clear that we can’t agreed to a withdrawal agreement without a precise future framework which delivers the future trade and security partnership which the Government wants.

“The PM said the UK would continue working hard in the talks on Brexit and the message from EU leaders is that they want to reach a deal.”

Meanwhile, the Prime Minister was warned that she faces a Commons rebellion of at least 40 Conservative MPs if she returns from Brussels with a deal based on her Chequers plan, leaving the UK “half in, half out” of the EU.

A revolt on this scale would leave Mrs May relying on the votes of dozens of Labour MPs to secure parliamentary approval for any deal.

Former Brexit minister Steve Baker said that as many as 80 Tories are ready to oppose the plan agreed by Cabinet at Mrs May’s country residence in July, and that at least half of them would stand firm against an “extremely hard” whipping operation.

Mr Baker, a senior figure in the hardline Brexiteer European Research Group, told BBC Radio 4’s Today programme: “The whips would be doing incredibly well if they were to halve the numbers.

“My estimate is that there are at least 40 colleagues who are not going to accept a half-in, half-out Chequers deal or indeed a backstop that leaves us in the internal market and the customs union, come what may.”

Conservative former chief whip Mark Harper warned that relying on Labour voters would not work.

Mr Harper, who was a Home Office minister during Mrs May’s tenure in the department, told the Daily Telegraph: “We are going to have to carry this deal on our own benches. If you’re the Prime Minister, you do have to listen to colleagues.”

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International Development Secretary Penny Mordaunt, who campaigned for Leave in the referendum, said Mrs May “has my support and I am not in any way expecting that situation to change”.

But she suggested that the Prime Minister may have to amend her Chequers plan to get a final deal, saying that “we don’t know where this is going to end up”.